Multivariate methods are described which improve the quality of the information which is extracted from inductively coupled plasma (ICP) atomic emission spectra. The enhancements provided by these methods result from using more of the spectral information than is used by simpler peak height measurement schemes. The detection limit of an analyte is significantly improved when mathematical treatment is applied to emission spectra at multiple wavelengths near the peak maximum compared to peak height measurements which make use of only one bandpass of information. The advantages of these multivariate methods are greatest in situations where spectral interferences are present at the analyte wavelength. These algorithms replace auxiliary background correction routines since a background profile can be fit to the unknown spectrum. Even very small wavelength registration errors can be corrected using numerical derivatives of the unknown spectrum as components in the linear model. In this paper, multivariate methods for ICP are developed using only the method of least squares (MLS). The method is applied to simulated spectra and to real spectra collected on the Plasma 2000 spectrometer. A trace level determination of cobalt in the presence of an interfering concentration of iron is demonstrated at the 238.892-nm cobalt line.